迭代算法逼近严格伪压缩映象最小范数不动点与变分不等式解  

An Iterative Algorithm for Minimum-norm Fixed Points of Strict Pseudo-contraction and Solutions to a Variational Inequality

作　　者：徐卫[1] 李冰冰[1] 屠国燕[1] 董力强[1] 

机构地区：[1]同济大学浙江学院,浙江嘉兴314001

出　　处：《嘉兴学院学报》2014年第6期58-63,共6页Journal of Jiaxing University

基　　金：浙江省教育厅科研项目(Y201330110)

摘　　要：在Hilbert空间中使用迭代格式xn+1=(1-αn)(δTxn+(1-δ)xn),n≥0来研究严格伪压缩映象T的最小范数不动点问题,采用新方法证明当参数满足适当条件时,序列x{n}强收敛至严格伪压缩映象T的最小范数不动点,同时该不动点也是某变分不等式的解.其结果推广与改进了一些近代相关结果.In this paper,we deal with an iterative algorithm for solving the minimum-norm fixed point problems of strict pseudo-contraction in Hilbert spaces by xn＋1 =（1-αn）（δTxn ＋（1-δ）xn）,where T：C →Cis a k-strict pseudo-contraction.Under certain approximate conditions,the sequence x{n}converges strongly to the minimum-norm fixed point of strict pseudo-contraction T,which is also a solution to a variational inequality.The results here extend and improve some recent related results.

关 键 词：最小范数不动点 严格伪压缩映象 变分不等式 度量投影 迭代算法 

分 类 号：O177[理学—数学]